Necessary and Sufficient Conditions for Delay-Dependent Asymptotic Stability of Linear Discrete Large Scale Time Delay Autonomous Systems

This paper offers new, necessary and sufficient conditions for delay–dependent asymptotic stability of the linear discrete large scale time delay systems. It has been shown that asymptotic stability this class of systems can be mapped to the asymptotic stability of the corresponding so called ith discrete SES systems. The order of the SES system is manifold lower than the order of the observed large scale systems. At that, it necessary to solve system of matrix equations whose solution always exists. Using the feature that the observed large scale system is finite-dimensional, necessary and sufficient condition of stability was derived independent of time-delay, which is based on the equivalent matrix of the system, whose order is considerably higher than the corresponding SES system. Numerical computations are presented for illustration.